Assessing closed-form approximations for underground cable earth impedances

Electromagnetic transients on underground power cables are highly influenced by the natural resistivity of the ground. Modeling earth-return impedances of a system may properly consider the resistive losses due to the imperfectly conducting ground. The problem here is that up-to-date there is no general criteria for selecting an adequate earth-model for each specific cable system configuration. To obtain an exact uniform ground representation it is required to solve the Pollaczek integral, which does not possess an analytic closed-form solution. Recently, the author developed an accurate algorithmic solution to it. In this paper, this solution is applied in the numerical assessment of some of the most often-used earth-return impedance closed-form approximations. Recommendations regarding their accuracy ranges as well as contour error maps on the normalized ξ-η plane are provided. Finally, the impact of different approximation degrees on a calculated cable transient is shown by means of an application example.